Applied Mathematics & Optimization

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Large Deviations for Stochastic Evolution Equations with Small Multiplicative Noise
Applied Mathematics & Optimization - Tập 61 - Trang 27-56 - 2009
Wei Liu
The Freidlin-Wentzell large deviation principle is established for the distributions of stochastic evolution equations with general monotone drift and small multiplicative noise. As examples, the main results are applied to derive the large deviation principle for different types of SPDE such as stochastic reaction-diffusion equations, stochastic porous media equations and fast diffusion equations...... hiện toàn bộ
Construction of branching diffusion processes and their optimal stochastic control
Applied Mathematics & Optimization - Tập 7 - Trang 11-33 - 1981
S. Ustunel
In this work we construct a branching diffusion process whose “individuals” are interdependent, as the unique solution of a martingale problem. As an application we propose and solve a closed loop, finite horizon optimal control problem.
Backward stochastic differential equations and applications to optimal control
Applied Mathematics & Optimization - Tập 27 - Trang 125-144 - 1993
Shige Peng
We study the existence and uniqueness of the following kind of backward stochastic differential equation, $$x(t) + \int_t^T {f(x(s),y(s),s)ds + \int_t^T {y(s)dW(s) = X,} }$$ under local Lipschitz condition, where (Ω, ℱ,P, W(·), ℱt) is a standard Wiener process, for any given (x, y),f(x, y, ·) is an ℱt-a...... hiện toàn bộ
Long-Time Stabilization of Solutions to a Nonautonomous Semilinear Viscoelastic Equation
Applied Mathematics & Optimization - Tập 73 - Trang 251-269 - 2015
Hassan Yassine, Ali Abbas
We study the long-time behavior as time goes to infinity of global bounded solutions to the following nonautonomous semilinear viscoelastic equation: $$\begin{aligned} |u_t |^\rho u_{tt} -\Delta u_{tt}-\Delta u_{t}-\Delta u +\int ^\tau _0 k(s) \Delta u(t-s)ds+ f(x,u)=g, \ \tau \in \{t, \infty \}, \end{aligned}$$ ...... hiện toàn bộ
Shape Optimization in Viscous Compressible Fluids
Applied Mathematics & Optimization - Tập 47 - Trang 59-78 - 2002
Feireisl
Abstract. We present a method for solving the optimal shape problems for profiles surrounded by viscous compressible fluids. The class of admissible profiles is quite general including the minimal volume condition and a constraint on the thickness of the boundary. The fluid flow is modelled by the Navier—Stokes system for a general viscous barotropic fluid.
Second-Order Necessary Conditions for a Strong Local Minimum in a Control Problem with General Control Constraints
Applied Mathematics & Optimization - Tập 80 - Trang 135-164 - 2017
Hélène Frankowska, Nikolai P. Osmolovskii
We establish some second-order necessary optimality conditions for strong local minima in the Mayer type optimal control problem with a general control constraint $$U \subset \mathrm{I\! R}^m$$ and final state constraint described by a finite num...... hiện toàn bộ
Hölder Continuity and Optimal Control for Nonsmooth Elliptic Problems
Applied Mathematics & Optimization - Tập 60 Số 3 - Trang 397-428 - 2009
Robert Haller‐Dintelmann, Christian Meyer, Joachim Rehberg, Anton Schiela
Weak Convergence of Interacting SDEs to the Superprocess
Applied Mathematics & Optimization - Tập 41 - Trang 111-128 - 2000
A. Bose, P. Sundar
A finite system of stochastic differential equations defined on a lattice with nearest-neighbor interaction is scaled so that the distance between lattice sites decreases and the size of the system increases. The space—time process defined by the above system is shown to converge in law to the solution of the SPDE associated with the super-Brownian motion on [0, 1] .
Analysis of the Finite-State Ergodic Master Equation
Applied Mathematics & Optimization - Tập 87 - Trang 1-53 - 2023
Asaf Cohen, Ethan Zell
Mean field games model equilibria in games with a continuum of players as limiting systems of symmetric n-player games with weak interaction between the players. We consider a finite-state, infinite-horizon problem with two cost criteria: discounted and ergodic. Under the Lasry–Lions monotonicity condition we characterize the stationary ergodic mean field game equilibrium by a mean field game syst...... hiện toàn bộ
Abstract estimates of the rate of convergence for optimal control problems
Applied Mathematics & Optimization - - 1997
Tommi Kärkkäinen, Tiina Räisänen
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